Elastic property measurement using Rayleigh-Lamb waves

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Characterization of single crystal silicon and electroplated nickel films by uniaxial tensile test with in situ X-ray diffraction measurement

In this study, mechanical properties of micron‐thick single crystalline silicon (Si) and electroplated nickel (Ni) films at intermediate temperatures are investigated by means of X‐ray diffraction (XRD) tensile testing. The developed tensile test technique enables us to directly measure lateral (out‐of‐plane) elastic strain of microscale crystalline specimen using XRD during tensile loading, and determines Young's modulus, Poisson's ratio and tensile strength of the Si and Ni specimens. The specimens, measuring 10 μm thick, 300 μm wide and 3 mm long, are prepared through a conventional micro‐machining process, and the ultraviolet lithographie galvanoformung abformung (UV‐LIGA) process including a molding and an electroplating. The Si specimens, showing brittle fracture at room temperature (R.T.), have average Young's modulus and Poisson's ratio of 169 GPa and 0.35, respectively, in very good agreement with analytical values. The Ni specimens, showing ductile fracture, have those of 190 GPa and 0.24, lower than bulk coarse grained Ni. Young's moduli of both the Si and Ni specimens decrease with increasing temperature, but Poisson's ratios are independent of temperature. The influence of specimen size on elastic‐plastic properties of the specimens is discussed.     

Low-temperature elastic properties of four wrought and annealed aluminium alloys

The elastic properties of four annealed polycrystalline commercial aluminium alloys were studied between 4 and 300 K using a pulse-superposition method. Results are given for longitudinal sound velocity, transverse sound velocity, Young's modulus, shear modulus, bulk modulus (reciprocal compressibility), Poisson's ratio, and elastic Debye temperature. The elastic stiffnesses of the alloys increase 4 to 13% on cooling from room temperature to liquid helium temperature. The elastic constant-temperature curves exhibit regular behaviour.     

A resonant method for determining mechanical properties of Si3N4 and SiO2 thin films

This study investigates the measurement of Poisson's ratio and Young's modulus of silicon dioxide (SiO₂) and silicon nitride (Si₃N₄) thin films using a resonant method. Two thin films, which are SiO₂ and Si₃N₄, are fabricated as the specimens of microcantilever beams and plates using the bulk micromachining. The resonant frequency of the cantilever beams and plates is measured using a laser interferometer. The Young's modulus of thin films can be calculated from the resonant frequency of the cantilever beams, and the Poisson's ratio of thin films is determined by the frequency of the cantilever plates. Experimental results show that the Poisson's ratios of SiO₂ and Si₃N₄ are 0.16 and 0.26, respectively, and the Young's moduli of SiO₂ and Si₃N₄ are, respectively, 55.6 GPa and 131.6 GPa.     

Holographische Schwingungsanalyse zur Bestimmung der elastischen Konstanten anisotroper Verbundwerkstoffe

Evaluation of Elastic Constants of Anisotropic Composite Materials by Means of Holographic Vibration Analysis . The wellknown ?plate-equation”? describing vibrations of thin, homogeneous and isotropic plates is reformulated for nonisotropic composites, and equations are derived for to determine elastic constants. If type and frequency of the natural vibrations are known from holographic interferometry and one of the elastic constants — for instance Poisson's number — is given or determined somehow else all other constants can be calculated.     

Buckling analysis of composite plates using moving least squares differential quadrature method

This work concerns with buckling and vibration analysis of composite plates based on a transverse shear theory. A numerical scheme is introduced to determine the angular frequencies and critical buckling loads of such plates. Moving least square differential quadrature method is employed to reduce the problem to that of eigen value problem. The accuracy and efficiency of the proposed scheme is examined with different computational characteristics, (radius of support domain, basis completeness order, and scaling factors). The obtained results agreed, at less execution time, with the previous ones. Further, a parametric study is introduced to investigate the influence of elastic and geometric characteristics, (Young's modulus gradation ratio, shear modulus gradation ratio, Poisson's ratio, loading parameter, and aspect ratio), of the composite on the values of critical buckling load, natural frequencies, and behavior of mode shape functions.     

How isotropic are quasi-isotropic laminates

The concept of quasi-isotropic laminates is very well documented in literature. Essentially, the laminate consists of laminae with fibers at equal angular spacing. The theoretical analysis of these laminates, based on the laminate theory, suggests that the elastic properties of the laminate will be isotropic. It is obvious that the theory makes some simplifying assumptions and hence the question remains that if this laminate is not really isotropic then how much anisotropic is it? Presented here is the experimental determination of the elastic modulus of a quasi-isotropic laminate [0/45/−45/90]_S by tensile mechanical testing and corroborated by a newly developed automated ultrasonic Lamb wave measurement. The Lamb wave velocity measurement in frequency domain is used to estimate the in-plane elastic constants: elastic modulus and the Poisson's ratio, non-destructively. The ultrasonic method provides a non-invasive and non-damaging method for the measurement.     

Poisson's ratios in glass fibre reinforced plastics

The characterisation of the mechanical properties of an orthotropic composite material generally requires nine interdependent elastic constants: three Young's moduli, three shear moduli and three Poisson's ratios. In most papers it is the practice to quote only two orthogonal axial moduli, a shear modulus and a Poisson's ratio in the plane of the laminate. However, the value of Poisson's ratio is a function of the orientation of the loading axis relative to the principal axis of the reinforcement fibres, both in and through the plane of the laminate. In an earlier paper, the correlation of experimental and theoretically predicted Poisson's ratios was reported around the angles in the plane of the laminate. Both unidirectional and woven roving fibreglass panels were tested. Accurate prediction of Poisson's ratio was shown to be critically dependent on the value of shear modulus used. This paper reports an extension of the previous work to consider the through-plane properties and will examine the results in the context of the Lempriere constraints.     

Critical Assessment 18: elastic and thermal properties of porous materials – rigorous bounds and cross-property relations

A critical assessment of model relations describing the porosity dependence of elastic properties (Young's modulus) and thermal properties (thermal conductivity) is given. It is shown that there are essentially five types of admissible predictive model relations for the relative Young's modulus and thermal conductivity of isotropic porous materials. The cross-property relations resulting from the complete analogy between the model relations for the elastic moduli and thermal conductivity of isotropic porous materials are reviewed and compared. Finally, it is shown that the fact that relative Young's moduli are not equal to relative thermal conductivities except for materials with translational symmetry, i.e. the mere existence and necessity of non-trivial cross-property relations, proves so-called minimum solid area models to be wrong.     

First principles predictions on mechanical and physical properties of HoX (X = As,P)

In this study, the calculated results of the structural, electronic, elastic, lattice dynamic, and thermodynamic properties of HoX (X = As, P) in rocksalt structure (B1) are presented. Ab initio calculations were performed based on density-functional theory using the Vienna Ab initio Simulation Package (VASP). Calculated structural parameters, such as the lattice constant, bulk modulus and its pressure derivative, cohesive energy, second-order elastic constants, electronic band structures and related total and partial density of states, Zener anisotropy factor, Poisson's ratio, Young's modulus, and isotropic shear modulus are presented. In order to gain further information, we investigated the pressure and temperature dependent behavior of the volume, bulk modulus, thermal expansion coefficient, heat capacity, entropy, Debye temperature, and Grüneisen parameter over a pressure range of 0–32 GPa and a wide temperature range of 0–2000 K. The phonon frequencies and one-phonon density of states are also presented.     

The elastic properties of nanostructured Ag measured by laser ultrasonic technique

The elastic properties of nanostructuredAg (ns-Ag) and its changing behavior during densification and annealing were investigated by a laser ultrasonic technique. The ns-Ag with grain size d about 30 nm was synthesized by inert gas condensation and in-situ compaction. The experimental results indicate that the Poisson's ratio, and the shear as well as the Young's modulus for all ns-Ag specimens investigated are smaller than the corresponding values for polycrystalline Ag (p-Ag). It was found that the change of the Poisson's ratio with the density is non-monotonic. It decreases with decreasing density as the relative density is higher than ~93%, below which it increases with decreasing density. We found that the increase of elastic modulus with density is nonlinear. It exhibits three-stage behavior: (i) a rapid descent stage, when the relative density D < ~93%; (ii) a relatively stable stage (93% <D < 95%), and (iii) a rapid ascent stage (D > 95%). In addition, for annealed specimens, the modulus decreases with increasing annealing temperature. It is similar to the density change during annealing, while the variation of the Poisson's ratio resembles more the changing behavior of the grain size of ns-Ag. All these results were discussed based on the microstructural characteristics of ns-Ag.     

A generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures

A generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described. Here dynamic analysis is understood as transient analysis and frequency response analysis. The generalized complex eigenvector method is based on finite element discretization of structure, approximation of viscoelastic properties by differential operators and mode superposition technique. Coefficients of differential operator are defined from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of differential operator in preset frequency range. Advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range. Also, the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions (complex Young's modulus, complex Poisson's ratio). The method is verified with the help of comparing with solutions obtained by complex modulus method. An influence of viscoelastic Poisson's ratio on transient and frequency responses of structure is demonstrated. Copyright © 2001 John Wiley & Sons, Ltd.     

Lamb waves in a thin isotropic layer between two anisotropic layers

Attenuative Lamb wave propagation in adhesively bonded anisotropic composite plates is introduced. The isotropic adhesive exhibits viscous behavior to stimulate the poor curing of the middle layer. Viscosity is assumed to vary linearly with frequency, implying that attenuation per wavelength is constant. Attenuation can be implemented in the analysis through modification of elastic properties of isotropic adhesive. The new properties become complex, but cause no further complications in the analysis. The characteristic equation is the same as that used for the elastic plate case, except that both real and imaginary parts of the wave number (i.e., the attenuation) must be computed. Based on the Lowe's solution in finding the complex roots of characteristic equation, the effect of longitudinal and shear attenuation coefficients of the middle adhesive layer on phase velocity dispersion curves and attenuation dispersion curves of Lamb waves propagating in bonded anisotropic composites is visualized numerically.     

Mechanical and electronic properties of Ag3Sn intermetallic compound in lead free solders using ab initio atomistic calculation

First principle calculations based on density functional theory (DFT) are used to calculate the structural, elastic and electronic properties of tin–silver intermetallic compound (Ag₃Sn), found mainly in lead free solder joints. In present work, for the exchange-correlation energy, generalized gradient approximation (GGA) functional is used. The calculated lattice constants are found to be within 2% error of the experimental values. All single crystal elastic constants are computed from which values of shear modulus, bulk modulus, Young's modulus and Poisson's ratio for polycrystalline Ag₃Sn are calculated using Voigt and Hill approximations. To explain the scatter in the experimentally determined values of elastic constants, directional dependence of bulk modulus and Young's modulus are estimated. The values of Young's modulus calculated along different planes are found to be in same range as experimentally determined values. Various anisotropic indices like universal anisotropic index, Zener anisotropic index, shear anisotropic index and others are calculated to study elastic anisotropy. Further anisotropy in Poisson's ratio is studied by calculating their values along six lower-index planes. The value of Debye temperature calculated using elastic data of present work is found be to higher than the values obtained using resistivity measurement, which can be attributed to temperature dependence. Electronic properties are studied via the band structure and total and partial density of states. The density of state (DOS) of Ag₃Sn has a characteristic main peak which is mainly dominated by Ag-d states. At the Fermi level, the total DOS value is found to be 1.97 states/eV with major contribution coming from Sn p states and minor contribution from Sn s and Ag s, p and d states.     

Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method

In this paper, a version of meshless local Petrov–Galerkin (MLPG) method is developed to obtain three-dimensional (3D) static solutions for thick functionally graded (FG) plates. The Young's modulus is considered to be graded through the thickness of plates by an exponential function while the Poisson's ratio is assumed to be constant. The local symmetric weak formulation is derived using the 3D equilibrium equations of elasticity. Moreover, the field variables are approximated using the 3D moving least squares (MLS) approximation. Brick-shaped domains are considered as the local sub-domains and support domains. In this way, the integrations in the weak form and approximation of the solution variables are done more easily and accurately. The proposed approach to construct the shape and the test functions make it possible to introduce more nodes in the direction of material variation. Consequently, more precise solutions can be obtained easily and efficiently. Several numerical examples containing the stress and deformation analysis of thick FG plates with various boundary conditions under different loading conditions are presented. The obtained results have been compared with the available analytical and numerical solutions in the literature and an excellent consensus is seen.     

Resonance acoustoelasticity measurement of stress in thin plates

A computer-driven, swept-frequency measurement technique is developed on the basis of resonance birefringence acoustoelasticity to evaluate the stresses in thin plates. The resonance frequency depends on the thickness and the elastic wave velocity; they change with stress because of the Poisson effect and the acoustoelastic effect. The resonance frequency is obtained from the spectral response curve in the electric impedance of the piezoelectric transducer. The frequency displacement induced by acoustically coupling the transducer can be minimized by employing the resonance peak closest to the transducer fundamental frequency. To illustrate the method, the residual stress is measured in butt-welded aluminum alloy plates and is compared with the results of conventional methods.     

Shear waves in a fluid saturated elastic plate

In the present context, we consider the propagation of shear waves in the transverse isotropic fluid saturated porous plate. The frequency spectrum for SH-modes in the plate has been studied. It is observed that the frequency of the propagation is damped due to the two-phase character of the porous medium. The dimensionless phase velocities of the shear waves have also been calculated and presented graphically. It is interesting to note that the frequency and phase velocity of shear waves in porous media differ significantly in comparison to that in isotropic elastic media.     

Dispersion of elastic waves in periodically inhomogeneous media

Propagation of time-harmonic elastic waves through periodically inhomogeneous media is considered. The material inhomogeneity exists in a single direction along which the elastic waves propagate. Within the period of the linear elastic and isotropic medium, the density and elastic modulus vary either in a continuous or a discontinuous manner. The continuous variations are approximated by staircase functions so that the generic problem at hand is the propagation of elastic waves in a medium whose finite period consists of an arbitrary number of different homogeneous layers. A dynamic elasticity formulation is followed and the exact phase velocity is derived explicitly as a solution in closed form in terms of frequency and layer properties. Numerical examples are then presented for several inhomogeneous structures.     

TC4负泊松比复合结构的人工骨力学性能调控研究

目的 基于不同变形机制的负泊松比结构优化设计新型复合多孔结构样件,增加力学性能的调控维度,以满足人体骨低弹性模量的匹配要求。方法 用内凹多边形替代手性结构的圆环,以获得新型的复合胞元结构。利用选区激光熔化成形技术制备负泊松比多孔人工骨样件,通过压缩实验揭示胞元结构类型、结构参数、孔隙率对屈服强度、弹性模量的影响规律,评测不同结构样件与人体骨间的力学性能匹配程度。结果 当孔隙率为65%～85%时,复合结构样件的成形质量、力学性能基本介于手性结构的和内凹结构的之间,且与孔隙率密切相关。手性结构、内凹结构和复合结构的弹性模量分别为2.39～4.64、1.12～3.77、1.01～3.47 GPa,屈服强度分别为65.19～223.06、45.25～195.81、26.54～143.58MPa。复合结构的弹性模量随环径和内凹角度的增大而减小。当孔隙率为75%时,环径由2.4 mm变至2.0 mm,弹性模量由2.651 GPa降低至2.082 GPa。当内凹角度由85°变至65°时,弹性模量则由3.566GPa降低至1.982GPa。结论 复合胞元结构可以融合材料特性,增加调控维度,进而匹配人工...